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Understanding Correlation: Measuring Linear Relationships Between Variables

Chapter 3.2 delves into correlation, showcasing how to measure the direction and strength of linear relationships between two quantitative variables using the correlation coefficient, denoted as r. The correlation analysis is vital as it highlights the relationship without distinguishing between explanatory and response variables. We explore practical examples, calculations, and the impact of outliers. Additionally, techniques for generating and interpreting scatterplots using calculators are discussed, providing hands-on experience in data analysis. Gain a comprehensive understanding of correlation through this insightful guide.

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Understanding Correlation: Measuring Linear Relationships Between Variables

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Presentation Transcript

  1. Chapter 3: Examining Relationships

  2. 3.2: Correlation • Measures the direction and strength of a linear relationship between two variables. • Usually written as r. • Video explaining how r is calculated • Fortunately, most of the time we will use our calculators!

  3. Example 1 – finding correlation by hand The following data represents the number of absences for 9 different students and their overall grade in the course. Find the correlation.

  4. Important facts about correlation: • Makes no distinction between explanatory and response variables • It doesn’t matter which variable is called x and which is called y • Requires that both variables be quantitative • For example, the correlation between the incomes of a group of people and what city they live in cannot be calculated because city is a categorical variable. • Because ruses standardized values of the observations, it does not change when we change the units of measurement of x, y, or both • r has no unit of measurement; it is just a number. • Positive r indicates positiveassociation and negative r indicates negative association.

  5. Important Facts about correlation: • r is always a number between -1 and 1 • Values near 0 indicate a very weak linear relationship • The strength increases as r moves toward -1 or 1. • Measures the strength of only a linear relationship • Does not describe curved relationships • ris not a resistant measurement • Use r with caution when there are outliers Note: ris not a complete description of two-variable data • Need to use the means and standard deviations of BOTHx and y along with the correlation when describing the data.

  6. Correlation Charts Correlation measures how closely related the data is to a linear approximation. The slope of the correlation gives the sign of the value.

  7. Make a Scatterplot • Use 2nd Y= • Turn plot 1 on • The first type of graph is a scatterplot • Xlist = L1 • Ylist = L2 • Press the zoom key then number 9

  8. Find the Correlation • First, make sure the diagnostics are turned on: • Press 2nd 0 • Brings up catalog • Find DiagnosticOn and press enter twice • Press the STAT key • Scroll over to CALC • Use either option 4 or 8

  9. Example 2 – Using the calculator • Using the data from example 1, find the correlation using your calculator. • STAT/CALC/LinReg • r = -.946

  10. Section 3.2 complete • Homework: p.142-146 #’s 24 (do part a by hand and for part b use lists to find r in your calc), 25, 26, 28, 34, 36, & 37

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